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iPhone 5S doesn't indicate when SIM card is removed

Check under iPhone Storage (might say Storage & iCloud Usage for iOS 10) in Settings > General and see if you see iOS 11 in the list that populates and if it’s there, tap it and delete it. It’ll look something like this after you tap it:

View attachment 40803

Sometimes the failed iOS update file gets stored on the phone and won’t let you update until you delete it. After deleting it (if it’s there), try updating again.
Thanks, I deleted the update and downloaded and installed again, but it failed again during the installation
 
Thanks, I deleted the update and downloaded and installed again, but it failed again during the installation

Well it seems that you have tried everything and it looks like it may be time for a new phone. Good luck with the new one if you end up going that route.
 
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